This is throwing everything and the kitchen sink at the paper in hopes it will stick.
Some of the criticism is specious and demonstrates its author's bias. For instance, it conflates speaking of a diagnosis with stigmatising sufferers and accusing someone who is studying a condition that frequently leads to medicalisation of treating the condition as a medical issue ("pathologising"). This is ludicrous, but typical for advocates of transgender ideology - they demand it not be seen as a medical issue while also demanding faster and better access to medical treatment.
Another criticism is that Littman did not define puberty or adolescence. This is trying to attack (and ultimately erase) the very clear distinction between the two cohorts of children who identify as trans.
The first group, well researched and documented for over 50 years, presents at a pre-school age and if the gender dysphoria resolves (when the child is said to desist), it typically does so at the onset of puberty.
The prevalence is about 6 in 100,000 children with the balance of males vs females at about 1.06 to 1, with slightly more boys being taken to see a professional before puberty and slightly more girls during or after puberty, but all of these children having displayed the signs and symptoms of gender dysphoria long before puberty begins. In those children who persist into adulthood and who are almost always homosexual, the sexes are also distributed quite evenly.
The second cohort is a new phenomenon, observed in the last fifteen years or so, all over the Westernised world. Children present well after the onset of puberty, often at a fairly late stage, without any prior warning (hence Rapid Onset Gender Dysphoria). Several children coming out as trans from the same friendship group is quite common, suggesting a prevalence of 1 in 100 or more, with girls outnumbering boys by between 2 : 1 to 9 : 1 (depending on what country you're looking at).
If these cohorts are indeed distinct, especially in regard to the imbalance of the sexes, this suggests that their gender dysphoria may also be of a different variety with potentially different causes. (Social contagion is an important factor in other conditions starting in adolescence, and would therefore have to be investigated as a possible mechanism to developing the condition.)
The threat this poses to the ideology is significant. It would suggest that gender identity is not innate and unchangeable, but could be subject to outside influences and impermanent (which in turn may mean it's treatable).
Hence most criticism of the hypothesis of ROGD is that the parents had simply been oblivious to their children's true gender and/or ignorant of the signs and symptoms of gender dysphoria and that these children had in actual fact always been trans, they just never felt comfortable enough to come out to the world. (The observed and statistically relevant imbalance between the sexes is inconvenient to this narrative, and therefore usually not addressed.)
The argument hinted at here, that the timing is wrongly labelled as in adolescence because parents don't understand what puberty is, is cute.
The argument that the study is invalid because most respondents were female, aged between 45 and 60 and white on the other hand is just stupid. It continues to be mostly mothers who deal with childcare issues, even if they are working. The average age that women have children has increased, making 45 to 60 a perfectly expected age group to have older teenagers. As for the criticised lack of diversity in ethnicity and education, the family background of most kids presenting with this suggested new form of gender dysphoria matches those of the respondents closely. This phenomenon seems to be less common amongst socially disadvantaged children.
There's loads more to scrutinise, yet I do hope that the author has also included some valid criticism coz that's a lot of effort otherwise for them, but at first glance that's what I've picked up on.